The polynomial `(ax^(2)+bx+c)(ax^(2)-dx-c),ac ne 0` , has :

Options

A. our real roots
B. at least two real roots
C. at most two real roots
D. No real roots

Answer

B

Explanation

Ler `D_(1) and D_(2)` be the discriminants of `ax^(2) + bx + c = 0 and ax^(2) - dx - c = 0` respectively. Then, `D_(1) = b^(2) - 4ac and D_(2) = d^(2) + 4ac`
`rArr" "D_(1) + D_(2) = b^(2) + d^(2) gt 0`
`rArr" ""At least one of" D_(1) and D_(2)` is positive.
Hence, at least one of the equations `ax^(2)+ bx + c = 0 and ax^(2) - dx - c = 0` has real roots.
Thus, the given polynomial has at least two real roots.